Issue 53

V. Rizov et alii, Frattura ed Integrità Strutturale, 53 (2020) 38-50; DOI: 10.3221/IGF-ESIS.53.04

where

3 0 x l   . (3) In (1) and (2), n b and n h are the width and height in the free end of the beam, the width and height in the clamping are denoted by t b and t h , 3 x is the longitudinal centroidal axis of the beam (Fig. 1).

Figure 1: Geometry and loading of inhomogeneous cantilever beam with linearly varying sizes of the cross-section in the length direction. The beam under consideration exhibits continuous (smooth) material inhomogeneity in both height and width directions of the cross-section. Thus, the distribution of the modulus of elasticity, E , in the beam cross-section is described by the following power law:

g

b y



      

f

z

1 2

  

  

3

2







3

T L E E E  

 

E E

E

,

(4)

  

  

S

L

L

b

h

where

b b y    , (5)

3

2

2

h h z    . (6)

3

2

2

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